Use OnObjectSave to perform a script that uses the Relookup Field Contents to trigger a relookup of the values.
This updates all the records in your current found set, so you may need to do additional work to update data in just the records you want to update. (If you only want o relookup values in the current record, there's a way to do that with a set field step.)
How would you incorporate that set field step?
Say you have this relationship:
LookUpTable::PrimaryKey = MainTable::ForeignKey
To relookup all fields that use a looked up value auto-enter setting based on this relationship, use this set field step:
Set Field [MainTable::ForeignKey ; Maintable::ForeignKey]